In a combinatorial search problem with binary tests, we are given a set of elements (vertices) and a hypergraph of possible tests (hyperedges), and the goal is to find an unknown target element using a minimum number of tests. We explore the expected test number of randomized strategies. Our main results are that the ratio of the randomized and deterministic test numbers can be logarithmic in the number of elements, that the optimal deterministic test number can be approximated (in polynomial time) only within a logarithmic factor, whereas an approximation ratio 2 can be achieved in the randomized case, and that optimal randomized strategies can be efficiently constructed at least for special classes of graphs.

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BibTeX @article{Damaschke2016,author={Damaschke, Peter},title={Deterministic versus randomized adaptive test cover},journal={Theoretical Computer Science},issn={0304-3975},volume={653},pages={42-52},abstract={In a combinatorial search problem with binary tests, we are given a set of elements (vertices) and a hypergraph of possible tests (hyperedges), and the goal is to find an unknown target element using a minimum number of tests. We explore the expected test number of randomized strategies. Our main results are that the ratio of the randomized and deterministic test numbers can be logarithmic in the number of elements, that the optimal deterministic test number can be approximated (in polynomial time) only within a logarithmic factor, whereas an approximation ratio 2 can be achieved in the randomized case, and that optimal randomized strategies can be efficiently constructed at least for special classes of graphs.},year={2016},keywords={combinatorial search, randomization, game theory, LP duality, set cover, fractional graph theory},}

RefWorks RT Journal ArticleSR ElectronicID 244807A1 Damaschke, PeterT1 Deterministic versus randomized adaptive test coverYR 2016JF Theoretical Computer ScienceSN 0304-3975VO 653SP 42OP 52AB In a combinatorial search problem with binary tests, we are given a set of elements (vertices) and a hypergraph of possible tests (hyperedges), and the goal is to find an unknown target element using a minimum number of tests. We explore the expected test number of randomized strategies. Our main results are that the ratio of the randomized and deterministic test numbers can be logarithmic in the number of elements, that the optimal deterministic test number can be approximated (in polynomial time) only within a logarithmic factor, whereas an approximation ratio 2 can be achieved in the randomized case, and that optimal randomized strategies can be efficiently constructed at least for special classes of graphs.LA engDO 10.1016/j.tcs.2016.09.019LK http://dx.doi.org/10.1016/j.tcs.2016.09.019OL 30